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.. _d-vec:
**d_vec.h** -- double precision vectors
===============================================================================
Memory management
--------------------------------------------------------------------------------
.. function:: double * _d_vec_init(slong len)
Returns an initialised vector of ``double``\s of given length. The
entries are not zeroed.
.. function:: void _d_vec_clear(double * vec)
Frees the space allocated for ``vec``.
Randomisation
--------------------------------------------------------------------------------
.. function:: void _d_vec_randtest(double * f, flint_rand_t state, slong len, slong minexp, slong maxexp)
Sets the entries of a vector of the given length to random signed numbers
with exponents between ``minexp`` and ``maxexp`` or zero.
Assignment and basic manipulation
--------------------------------------------------------------------------------
.. function:: void _d_vec_set(double * vec1, const double * vec2, slong len2)
Makes a copy of ``(vec2, len2)`` into ``vec1``.
.. function:: void _d_vec_zero(double * vec, slong len)
Zeros the entries of ``(vec, len)``.
Comparison
--------------------------------------------------------------------------------
.. function:: int _d_vec_equal(const double * vec1, const double * vec2, slong len)
Compares two vectors of the given length and returns `1` if they are
equal, otherwise returns `0`.
.. function:: int _d_vec_is_zero(const double * vec, slong len)
Returns `1` if ``(vec, len)`` is zero, and `0` otherwise.
.. function:: int _d_vec_is_approx_zero(const double * vec, slong len, double eps)
Returns `1` if the entries of ``(vec, len)`` are zero to within
``eps``, and `0` otherwise.
.. function:: int _d_vec_approx_equal(const double * vec1, const double * vec2, slong len, double eps)
Compares two vectors of the given length and returns `1` if their entries
are within ``eps`` of each other, otherwise returns `0`.
Arithmetic
--------------------------------------------------------------------------------
.. function:: void _d_vec_add(double * res, const double * vec1, const double * vec2, slong len2)
Sets ``(res, len2)`` to the sum of ``(vec1, len2)``
and ``(vec2, len2)``.
.. function:: void _d_vec_sub(double * res, const double * vec1, const double * vec2, slong len2)
Sets ``(res, len2)`` to ``(vec1, len2)`` minus ``(vec2, len2)``.
.. function:: void _d_vec_mul_2exp(double * res, const double * vec, slong len, int e)
Sets ``(res, len)`` to ``(vec, len)`` multiplied by `2^e`.
Dot product and norm
--------------------------------------------------------------------------------
.. function:: double _d_vec_dot(const double * vec1, const double * vec2, slong len2)
Returns the dot product of ``(vec1, len2)``
and ``(vec2, len2)``.
.. function:: double _d_vec_norm(const double * vec, slong len)
Returns the square of the Euclidean norm of ``(vec, len)``.
.. function:: double _d_vec_dot_heuristic(const double * vec1, const double * vec2, slong len2, double * err)
Returns the dot product of ``(vec1, len2)``
and ``(vec2, len2)`` by adding up the positive and negative products,
and doing a single subtraction of the two sums at the end. ``err`` is a
pointer to a double in which an error bound for the operation will be
stored.
.. function:: double _d_vec_dot_thrice(const double * vec1, const double * vec2, slong len2, double * err)
Returns the dot product of ``(vec1, len2)``
and ``(vec2, len2)`` using error-free floating point sums and products
to compute the dot product with three times (thrice) the working precision.
``err`` is a pointer to a double in which an error bound for the
operation will be stored.
This implements the algorithm of Ogita-Rump-Oishi. See
http://www.ti3.tuhh.de/paper/rump/OgRuOi05.pdf.
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